depends on the propagation direction of the spin waves, the relative direction of the magnetizations in the film and nanowire, and the geometry of the wire and film that is characterized by the form factor
\({\cal D}(k)=-2\mu _0\gamma \sqrt{{M_s\tilde{M}_s}/{\Lambda }}(1-e^{-|k|d})(1-e^{-|k|s})\sin \left({kw}/{2}\right)/{k^3}\) .
Here \(\Lambda \)  is the length of the magnetic wire. The spin waves in the film are circularly polarized when their wavelength is sufficiently short [1]}, [2]}, [3]}. Thereby when \(\phi =0\)  (\(\phi =\pi \) ), i.e. the magnetization of the wire and film is parallel (anti-parallel), the wire Kittel mode only couples with the spin waves of right-going (left-going) with \(g_{-|k|}=0\)  (\(g_{|k|}=0\) ) [1]}.
